I have one user that is complaining that his BlackBerry 7750 with 4.0 code (on BES 2.2.3.11 for Domino 6.5.4 HF2) is "losing" messages. He says several days of mail will disappear from the handheld, but not his mailbox.

I've checked everything and he seems to be setup like my other 230 users. Any ideas?

Have you checked his settings under Message->Options->General Options to see what the "Keep Messages" options is set to? The choices there are 15-30-60-90 days and forever.
Is he using the option to "Hide Filed messages" on the device when messages are moved into sub-folders in the Inbox?

You might also check the memory usage on the device. If it is full, it will delete older messages to make room for newer ones. I have seen this in a few devices and attributed it to a memory leak. If the device is out of memory, pull the battery to give it a hard reset. That should resolve the issue. Good luck.